Gradient-based optimal control of the non-Hermitian skin effect in optomechanical arrays

• URL: http://arxiv.org/abs/2609.04492v1
• Date: Thu, 03 Sep 2026 21:25:02 GMT
• Title: Gradient-based optimal control of the non-Hermitian skin effect in optomechanical arrays
• Abstract summary: Single-port non-Hermitian sensors impose a strict resource bound on metrological precision.<n>We test whether multi-port geometry can evade this resource bound by a double-chain opto ladder with opposing non-reciprocal amplification.<n>All solutions remain Hurwitz-stable under ty5percent disorder (qty87.5percent recovery), and the deep-stability advantage survives realistic noise.<n>The architecture enables subattonewton force sensing searches across the qtyrange110gigahertz band.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In single-port non-Hermitian sensors the Petermann factor offsets susceptibility gains, imposing a strict resource bound on metrological precision. We test whether a multi-port geometry can evade this bound: a double-chain optomechanical ladder with opposing non-reciprocal hoppings spatially separates signal amplification from quantum-noise drainage, and gradient-based differentiable optimal control (DOC) maximizes the resource-normalized Fisher information $\Fnorm$ subject to a Hurwitz-stability constraint. Across system sizes $N\in\{\num{6},\dots,\num{16}\}$ the optimizer returns $\Fnorm>0$ in every case, with two coexisting solution classes whose selection is initialization-dependent: deep-stability configurations achieve $\Fnorm\in\numrange{0.937}{0.987}$ with attenuated transmission, while marginal-stability configurations deliver directional gain $\Gfwd\in\qtyrange{13.5}{15.5}{\dB}$ with isolation $\Iso\in\qtyrange{40}{64}{\dB}$. A multi-restart ensemble reveals these classes are the endpoints of a precision--gain frontier. All solutions remain Hurwitz-stable under \qty{5}{\percent} disorder (\qty{87.5}{\percent} recovery), and the deep-stability advantage survives realistic preamplifier noise at $\Fnormeff\approx\num{0.3}$--$\num{0.5}$. Mapped onto circuit-QED parameters, the architecture enables sub-attonewton force sensing and broadband axion searches across the \qtyrange{1}{10}{\giga\hertz} band.

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